An $(\infty,2)$-categorical pasting theorem
Algebraic Topology
2023-10-04 v4 Category Theory
Abstract
We show that any pasting diagram in any -category has a homotopically unique composite. This is achieved by showing that the free 2-category generated by a pasting scheme is the homotopy colimit of its cells as an -category. We prove this explicitly in the simplicial categories model and then explain how to deduce the model-independent statement from that calculation.
Cite
@article{arxiv.2106.03660,
title = {An $(\infty,2)$-categorical pasting theorem},
author = {Philip Hackney and Viktoriya Ozornova and Emily Riehl and Martina Rovelli},
journal= {arXiv preprint arXiv:2106.03660},
year = {2023}
}
Comments
42 pages, comments welcome; v2: new section on related work with updated references; v3: moved the analysis of pushouts of Dwyer maps to arXiv:2205.02353 in order to prove a more general version of the result than is needed here; v4: final version